System of equations!
Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p+q+r is not equal to 0
x+ 2y – 3z = p
2x + 6y – 11z = q
x – 2y + 7z = r
Your options-
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5p –2q – r = 0
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5p + 2q + r = 0
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5p + 2q – r = 0
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5p – 2q + r = 0
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1 solution
If you haven't studied matrix ...try to reduce no. of variables ,
Equation (ii)-2(iii), 1 0 y − 2 5 z = q − 2 r . . . . ( i v )
Equation (ii)-2(i), 2 y − 5 z = q − 2 p o r , 1 0 y − 2 5 z = 5 q − 1 0 p . . . ( v )
Equation (iv) & (v) will have solution only if, q − 2 r = 5 q − 1 0 p ⇒ 5 p − 2 q − r = 0